The first part of this thesis investigates the growth of ion density perturbations in large-amplitude laser-driven wakefields via two-dimensional particle-in-cell simulations. Growth rates and wave numbers of the perturbations are found to be consistent with a longitudinal strong-field modulational instability. We examine the transverse dependence of the instability for a Gaussian wakefield envelope and show that growth rates and wave numbers can be maximised off- axis. On-axis growth rates are found to decrease with increasing ion mass or electron temperature. These results are in close agreement with theoretical predictions obtained by solving the dispersion relation for a long-wavelength electrostatic oscillation in resonance with the plasma frequency and energy density that is large compared to the plasma thermal energy density. The implications for wakefield accelerators – in particular multi-pulse schemes – and methods to mitigate the effects of ion dynamics are discussed.
In the second part of the thesis, we develop a linearised Fokker-Planck collision model for gyrokinetic simulations that satisfies conservation laws and is accurate at arbitrary collisionality. The differential test-particle component of the operator is exact; the implementation of the integrodifferential field-particle component uses a spherical harmonic expansion and a modified Laguerre polynomial expansion introduced by Hirshman and Sigmar [S. P. Hirshman, D. J. Sigmar, Phys. Fluids 19, 1532 (1976)]. The numerical methods of the implementation in the δf-gyrokinetic code stella [M. Barnes, F. I. Parra, M. Landreman, Journal of Comp. Phys. 391, 365-380 (2019)] are discussed, and conservation properties of the operator are verified. The accuracy of the collision model is demonstrated by computing transport coefficients for the classical Spitzer problem and by performing benchmarks against the collision model of the gyrokinetic solver GS2.</p
